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Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND NO. 2011-XXXXP

Kokkos: Enabling Performance Portability of C++ Applications and Libraries across Manycore Architectures

ORNL / January 29, 2015 SAND2015-0409 O (Unlimited Release)

Increasingly Complex Manycore Architectures ¿ Performance Portable and Future Proof Codes?

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PIM DDR

L2*

NVRAM

PIM

L1*

Tex

Scr

L1*

Tex

Scr

L1*

Tex

Scr

NIC L3

Memory Spaces - Bulk non-volatile (Flash?) - Standard DDR (DDR4) - Fast memory (HBM/HMC) - (Segmented) scratch-pad on die Execution Spaces - Throughput cores (GPU) - Latency optimized cores (CPU) - Processing in memory

Special Hardware - Non caching loads - Read only cache - Atomics

Programming models - GPU: CUDA-ish - CPU: OpenMP - PIM: ??

Vision for Heterogeneous Parallelism “MPI + X” Programming Model, separate concerns Inter-node: MPI and domain specific libraries layered on MPI Intra-node: Kokkos and domain specific libraries layered on Kokkos

Intra-node parallelism concerns: heterogeneity & diversity Execution spaces (CPU, GPU, PIM, ...) have diverse performance requirements Memory spaces have diverse capabilities and performance characteristics Vendors have diverse programming models for optimal utilization of their hardware

Standardized performance portable programming model? Via vendors’ (slow) negotiations: OpenMP, OpenACC, OpenCL, C++17 Vendors’ (biased) solutions: C++AMP, Thrust, CilkPlus, TBB, ArrayFire, ... Researchers’ solutions: HPX, StarPU, Bolt, Charm++, ...

Necessary condition: address execution & memory space diversity SNL Computing Research Center’s Kokkos (C++ library) solution Engagement with ISO C++ Standard committee to influence C++17

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Application and Domain Specific Library Layer

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Kokkos: A Layered Collection of C++ Libraries Applications and Domain Libraries written in Standard C++ Not a language extension like OpenMP, OpenACC, OpenCL, CUDA, ... Require C++1998 standard (supported everywhere except IBM’s old xlC) Prefer C++2011 for its concise lambda syntax Vendors are catching up to C++2011 language compliance

Kokkos implemented with C++ template meta-programming In spirit of TBB, Thrust & CUSP, C++AMP, ...

Back-ends: Cuda, OpenMP, pthreads, vendor libraries ...

Sparse Linear Algebra (Trilinos) Kokkos Containers Kokkos Core

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Performance Portability Challenge: Best (good) performance requires computations to implement architecture-specific memory access patterns CPUs (and Xeon Phi) Core-data affinity: consistent NUMA access (first touch) Array alignment for cache-lines and vector units Hyperthreads’ cooperative use of L1 cache

GPUs Thread-data affinity: coalesced access with cache-line alignment Temporal locality and special hardware (texture cache)

Array of Structures (AoS) vs. Structure of Arrays (SoA) dilemma This has been the wrong concern

The right question: Abstractions for Performance Portability?

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Kokkos Performance Portability Answer Integrated mapping of thread parallel computations and

multidimensional array data onto manycore spaces Kokkos maps users’ parallel computations to threads Standard parallel programming model pattern; e.g., parallel-for Users implement C++ functions or lambdas for their parallel loop bodies Kokkos calls user’s code from architecture’s “hardware” threads

Kokkos’ multidimensional array data structure has a twist Layout mapping: multi-index (i,j,k,...) ↔ memory location Kokkos chooses layout for architecture-specific memory access pattern Layout changes are invisible to user code IF user code honors Kokkos’ simple array API: a(i,j,k,...)

Polymorphic multidimensional array layout

... and utilizes special hardware invisibly to users’ code GPU texture cache to speed up read-only random access patterns Atomic operations for thread safety

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Projects leveraging Kokkos for MPI+X Albany : a Trilinos-based finite element application code Ice Sheet Modeling Computational Mechanics Quantum Device Design

Atmosphere Dynamics

Target Application for CAAR Proposal [Salinger et al.]

Kokkos integration in progress

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Projects leveraging Kokkos for MPI+X and points-of-contact for MPI+X transition effort Trilinos / Tpetra : foundational data structures and kernels for sparse linear

algebra; Mark Hoemmen, Christian Trott Trilinos / Stokhos : accelerating embedded UQ ; Eric Phipps LAMMPS : molecular dynamics; Christian Trott ASCR Multiphysics MHD; Roger Pawlowski and Eric Cyr FASTMath SciDAC / Graph Algorithms : Siva Rajamanickam Zoltan / Graph Coloring : fast threaded graph coloring to identify independent

sets of work for task parallelism; Erik Boman, Siva Rajamanickam EMPRESS and miniPIC : particle-in-cell ; Matt Bettencourt miniAero : CFD finite element mini-application ; Ken Franco miniContact : contact detection for solid mechanics ; Glen Hansen SHIFT @ ORNL; Steve Hamilton Kokkos SNL/LDRD Directed acyclic graph of internally data parallel (coarse-grain) tasks sparse matrix factorization and graph algorithm mini-applications

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Abstractions and Application Programmer Interface

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Spaces, Policies, and Patterns Execution Space : where functions execute Encapsulates hardware resources; e.g., cores, GPU, vector units, ...

Memory Space : where data resides AND what execution space can access that data Also differentiated by access performance; e.g., latency & bandwidth

Execution Policy : how (and where) a user function is executed E.g., data parallel range : concurrently call function(i) for i = [0..N) User’s function is a C++ functor or C++11 lambda

Pattern: parallel_for, parallel_reduce, parallel_scan, task, ...

Compose: pattern + execution policy + user function; e.g., parallel_for( Policy<Space>, Function);

Execute Function in Space according to parallel_for pattern and Policy

Extensible spaces, policies, and patterns (by expert developers)

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Examples of Execution and Memory Spaces

Compute Node

Multicore Socket DDR

Attached Accelerator

GPU GDDR

GPU::capacity (via pinned)

primary

primary

GPU::perform (via UVM)

Compute Node

Multicore Socket DDR

primary shared

deep_copy

Attached Accelerator

GPU GDDR primary

perform shared

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Multidimensional Array View API (simple) View< double**[3][8] , Space > a(“a”,N,M); Allocate array data in memory Space with dimensions [N][M][3][8] Each * indicates a runtime supplied dimension Proposing C++ standard adjustment to enable View<double[ ][ ][3][8],Space>

Kokkos chooses array layout appropriate for “Space”

a(i,j,k,l) : User’s access to array data Optional array bounds checking of indices in debug compile “Space” accessibility enforced; e.g., GPU code cannot access CPU memory

View Semantics: View<double**[3][8],Space> b = a ; A shallow copy: ‘a’ and ‘b’ are pointers to the same allocated array data Reference counting how many Views to the same data When reference count == 0 , automatically deallocates data

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View API: Deep Copy and Host Mirror deep_copy( destination_view , source_view ); Copy array data of ‘source_view’ to array data of ‘destination_view’ Kokkos policy: never hide an expensive deep copy operation Only deep copy when explicitly instructed by the user

Avoid expensive permutation of data due to different layouts Mirror the dimensions and layout in Host’s memory space

typedef class View<...,Space> MyViewType ; MyViewType a(“a”,...); MyViewType::HostMirror a_h = create_mirror( a ); deep_copy( a , a_h ); deep_copy( a_h , a );

Avoid unnecessary deep-copy MyViewType::HostMirror a_h = create_mirror_view( a );

If Space (might be an execution space) uses Host memory space then ‘a_h’ is simply a view of ‘a’ and deep_copy is a no-op

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View API (advanced) View<ArrayType,Layout,Space,Attributes> ArrayType: scalar type, # runtime dimensions, compile-time dimensions Layout: user can override Kokkos’ choice for layout Attributes: user’s access intentions

Why manually specify Layout ? Force compatibility with legacy code while incrementally porting Optimize performance with exotic layout

View<double**,Tile<8,8>,Space> m(“matrix”,N,N); Tiling layout hidden from user code m(i,j)

A “plug in” extension point

Access intent attributes Turn off reference counting to wrap an legacy code’s array Indicate const and random access to utilize GPU texture cache

View< const double **, Cuda, RandomAccess> b = a ; A “plug in” extension point

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Subview : View of a sub-array B = subview( A , ...range_and_index_argument_list... )

Challenging capability due to polymorphic array Layout Views are strongly typed: View<ArrayType,Layout,Space,Traits> Compatibility constraints on B’s type, A’s type, and argument list runtime and compile-time dimensions number and type (range or index) of calling arguments array layout ‘const-ness’ and other memory access traits

C++11 ‘auto’ capability simplifies use auto B = subview( A , ...range_and_index_argument_list... );

Let implementation choose a compatible View type Caution: View’s data may become non-contiguous

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Parallel Execution API (simple with C++11) AXPY example using C++11 lambda

parallel_for( N , KOKKOS_LAMBDA( int i ) { y(i) = alpha * x(i) + y(i); } ); User functor via C++11 lambda expression Default execution space and range policy i = [0..N) Kokkos chooses which threads call function with each value of ‘i’

DOT example using C++11 lambda parallel_reduce( N , KOKKOS_LAMBDA( int i , double & value ) { value += x(i) * y(i); } , result ); Kokkos manages thread-local temporaries Kokkos manages scalable inter-thread reduction

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Parallel Execution API parallel_pattern( Policy<Space> , Function )

User Function: C++11 Lambda or C++ Functor Use a functor with non-trivial function bodies

struct UserAXPY { double alpha ; View<double*,Space> x , y ; // “calling arguments” KOKKOS_INLINE_FUNCTION void operator()( int i ) const { y(i) = alpha * x(i) + y(i); } // function };

Multi-function User Functor capability When more than one function shares the same “calling arguments” Migration to Kokkos: incrementally add parallel functions to existing classes

Execution Policy : flexibility & extensibility RangePolicy : i = [0..N) TeamPolicy : two-level parallelism with team collectives and shared memory Portable access to Cuda thread grid, block, and shared memory

TaskPolicy : experimental using SNL’s Qthreads runtime

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Atomic operations atomic_exchange, atomic_compare_exchange_strong, atomic_fetch_add, atomic_fetch_or, atomic_fetch_and

Thread-scalability of non-trivial algorithms and data structures Essential for lock-free implementations Concurrent summations to shared variables E.g., finite element computations summing to shared nodes

Updating shared dynamic data structure E.g., append to a shared array or insert into a shared map

Portably map to compiler/hardware specific capabilities GNU and CUDA extensions when available Current: any 32bit or 64bit type, may use CAS-loop implementation Future: any data type via “sharded lock” pattern

ISO/C++ 2011 and 2014 standards not adequate for HPC Proposal in for 2017 standard to address this gap

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Performance Evaluation

Evaluate Performance Impact of Array Layout

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Molecular dynamics computational kernel in miniMD Simple Lennard Jones force model: Atom neighbor list to avoid N2 computations

Test Problem 864k atoms, ~77 neighbors 2D neighbor array Different layouts CPU vs GPU Random read ‘pos’ through

GPU texture cache Large performance loss

with wrong array layout

Fi= ∑j , rij< r cut

6 ε[(ςrij)7

− 2(ςr ij)13]

pos_i = pos(i); for( jj = 0; jj < num_neighbors(i); jj++) { j = neighbors(i,jj); r_ij = pos_i – pos(j); //random read 3 floats if (|r_ij| < r_cut) f_i += 6*e*((s/r_ij)^7 – 2*(s/r_ij)^13) } f(i) = f_i;

0

50

100

150

200

Xeon Xeon Phi K20x

GFl

op/s

correct layout(with texture)

correct layout(without texture)

wrong layout(with texture)

Evaluate Performance Overhead of Abstraction Kokkos competitive with native programming models

MiniFE: finite element linear system iterative solver mini-app

Compare to versions specialized for programming models

Running on hardware testbeds

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048

12162024

K20X IvyBridge SandyBridge XeonPhi B0 XeonPhi C0 IBM Power7+

MiniFE CG-Solve time for 200 iterations on 200^3 mesh

NVIDIA ELL NVIDIA CuSparse Kokkos OpenMPMPI-Only OpenCL TBB Cilk+(1 Socket)

Tim

e (s

econ

ds)

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Kokkos’ Unordered Map (a.k.a. Hash Map) Thread scalable fill

Lock-free implementation with minimal use of atomics API deviates from C++11 unordered map

No on-the-fly allocation / reallocation Index-based instead of iterator-based

Insert (fill) within a parallel reduce functor Within the functor: {status, index} = map.insert(key,value);

Status = success | existing | failed due to insufficient capacity Parallel reduce the failed-count to resize the map

Algorithmic use: UnorderedMap<Key,Value,Space> map ; do { map.rehash( capacity ); capacity += ( nfailed = parallel_reduce( N , functor ) ); } while( nfailed ); // should iterate at most twice

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Unordered Map Performance Evaluation Parallel-for insert to 88% full with 16x redundant inserts

NW= number attempts to insert = Capacity * 88% * 16 Near – contiguous work indices [iw,iw+16) insert same keys Far – strided work indices insert same keys

Single Accelerator Performance Tests NVidia Kepler K40X, 12Gbytes Intel Xeon Phi (Knights Corner) COES2, 61 cores, 1.2 GHz, 16Gbytes Limit use to 60 cores, 4 hyperthreads/core

0

5

10

15

20

1E+04 1E+05 1E+06 1E+07

nano

sec

/ at

tem

pted

in

sert

map capacity

Phi-240, far

Phi-240, near

K40X, far

K40X, near

K40X dramatically better performance Xeon Phi implementation

optimized using explicit non-caching prefetch Theory: due to cache

coherency protocols and atomics’ performance

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MiniFENL Proxy Application Solve nonlinear finite element problem via Newton iteration

Focus on construction and fill of sparse linear system Thread safe, thread scalable, and performant algorithms Evaluate thread-parallel capabilities and programming models

Construct sparse linear system graph and coefficient arrays Map finite element mesh connectivity to degree of freedom graph Thread-scalable algorithm for graph construction

Compute nonlinear residual and Jacobian Thread-parallel finite element residual and Jacobian Atomic-add to fill element coefficients into linear system

Atomic-add for thread safety, performance?

Solve linear system for Newton iteration

Thread-Scalable Fill of Sparse Linear System

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MiniFENL: Newton iteration of FEM: 𝒙𝒏+𝟏 = 𝒙𝒏 − 𝑱−𝟏(𝒙𝒏)𝒓(𝒙𝒏�

Fill sparse matrix via Scatter-Atomic-Add or Gather-Sum ? Scatter-Atomic-Add

+ Simpler + Less memory – Slower HW atomic

Gather-Sum + Bit-wise reproducibility

Performance win? Scatter-atomic-add ~equal Xeon PHI 40% faster Kepler GPU

Pattern chosen Feedback to HW vendors:

performant atomics

00.05

0.10.15

0.20.25

0.30.35

1E+03 1E+04 1E+05 1E+06 1E+07Mat

rix F

ill: m

icro

sec/

node

Number of finite element nodes

Phi-60 GatherSumPhi-60 ScatterAtomicPhi-240 GatherSumPhi-240 ScatterAtomicK40X GatherSumK40X ScatterAtomic

Thread-Scalable Sparse Matrix Construction MiniFENL: Construct sparse matrix graph from FEM connectivity Thread scalable algorithm for constructing a data structure

1. Parallel-for : fill Kokkos lock-free unordered map with FEM node-node pairs 2. Parallel-scan : sparse matrix rows’ column counts into row offsets 3. Parallel-for : query unordered map to fill sparse matrix column-index array 4. Parallel-for : sort rows’ column-index subarray

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0

0.5

1

1.5

2

1E+03 1E+04 1E+05 1E+06 1E+07

Mic

rose

c/no

de

Number of finite element nodes

Phi-60

Phi-240

K40X

Pattern and tools generally applicable to construction and dynamic modification of data structures

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Porting in Progress: Trilinos Suite Trilinos : SNL’s suite of equation solver libraries (and others) Previously MPI-only parallel Incremental refactoring to MPI+Kokkos parallel

Tpetra : Trilinos’ core parallel sparse linear algebra library Vectors, multi-vectors, sparse matrices, parallel data distribution maps Fundamental operations: axpy, dot, matrix-vector multiply, ... Templated on “scalar” type: float, double, automatic differentiation (AD),

embedded uncertainty quantification (UQ), ...

Port Tpetra to MPI+Kokkos, other libraries follow On schedule to complete in Spring 2015 Use of NVIDIA’s unified virtual memory (UVM) expedited porting effort

Embedded UQ already Kokkos-enabled through SNL/LDRD Greater computational intensity leads to significant speed-ups compared to

non-embedded UQ sampling algorithms

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Porting in Progress: LAMMPS LAMMPS : molecular dynamics application Fully MPI-only parallel with some (prototype) thread-parallel user packages Architecture specific with redundantly implemented physics

Incrementally refactoring to MPI+Kokkos parallel Goal: collapse redundantly implemented physics into “core” code base

MPI+Kokkos performing as well or better than thread-parallel user packages

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Takeaways : MPI + Kokkos for hybrid parallel Performance portability across diverse manycore architectures Compose : pattern + policy + function + polymorphic array layout to obtain architecture-appropriate memory access patterns AoS versus SoA dilemma is a non-issue, with the right abstractions Extensibility of patterns, policies, spaces, and array layout abstractions

=> future proofing versus architectural evolution?

Negligible performance overhead versus native implementation

R&D now addressing more challenging algorithms Dynamic data structures Task-dag and hybrid task-data parallelism Graph analytics algorithms

Transition of legacy codes in progress

Kokkos to be available via GitHub in FY15/Q3